A New Multi-wing Chaotic System and Its Fractional-Order Form

2016 ◽  
pp. 98-107
Author(s):  
Zengqiang Chen ◽  
Leilei Zhou ◽  
Jian Ma ◽  
Zhonglin Wang ◽  
Qing Zhang
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Form

A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order form

2017 ◽  
Vol 99 ◽  
pp. 209-218 ◽  
Author(s):  
Sifeu Takougang Kingni ◽  
Viet-Thanh Pham ◽  
Sajad Jafari ◽  
Paul Woafo
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Infinite Number ◽  
Equilibrium Points ◽  
Order Form

A chaotic system with equilibria located on a line and its fractional-order form

2022 ◽  
pp. 35-62
Author(s):  
Karthikeyan Rajagopal ◽  
Fahimeh Nazarimehr ◽  
Alireza Bahramian ◽  
Sajad Jafari
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Form

Multiscroll chaotic system with sigmoid nonlinearity and its fractional order form with synchronization application

2019 ◽  
Vol 116 ◽  
pp. 262-272 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Ali Durdu ◽  
Sajad Jafari ◽  
Yilmaz Uyaroglu ◽  
Anitha Karthikeyan ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Form

A Three-Dimensional No-Equilibrium Chaotic System: Analysis, Synchronization and Its Fractional Order Form

2017 ◽  
pp. 449-470 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Sundarapandian Vaidyanathan ◽  
Christos K. Volos ◽  
Ahmad Taher Azar ◽  
Thang Manh Hoang ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
System Analysis ◽  
Three Dimensional ◽  
Order Form

Dynamics, Circuit Design, Synchronization, and Fractional-Order Form of a No-Equilibrium Chaotic System

2018 ◽  
pp. 1-31 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Sundarapandian Vaidyanathan ◽  
Christos Volos ◽  
Xiong Wang ◽  
Vo Hoang Duy ◽  
...  
Keyword(s):  
Circuit Design ◽  
Fractional Order ◽  
Chaotic System ◽  
Order Form

Dynamics, Synchronization and Fractional Order Form of a Chaotic System With Infinite Equilibria

2018 ◽  
pp. 475-502 ◽  
Author(s):  
Viet–Thanh Pham ◽  
Gokul P.M. ◽  
Tomasz Kapitaniak ◽  
Christos Volos ◽  
Ahmad Taher Azar
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Form

scholarly journals Dynamics, Circuit Design and Fractional-Order Form of a Modified Rucklidge Chaotic System

2018 ◽  
Vol 1090 ◽  
pp. 012038
Author(s):  
A Sambas ◽  
S Vaidyanathan ◽  
M Mamat ◽  
M Sanjaya WS ◽  
S H Yuningsih ◽  
...  
Keyword(s):  
Circuit Design ◽  
Fractional Order ◽  
Chaotic System ◽  
Order Form

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

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